Rationality and fusion rules of exceptional $mathcal {W}$-algebras

HANDLE Open Access

Abstract

First, we prove the Kac–Wakimoto conjecture on modular invariance of characters of exceptional affine $mathcal {W}$-algebras. In fact more generally we prove modular invariance of characters of all lisse $mathcal {W}$-algebras obtained through Hamiltonian reduction of admissible affine vertex algebras. Second, we prove the rationality of a large subclass of these $mathcal {W}$-algebras, which includes all exceptional $mathcal {W}$-algebras of type $mathcal {A}$ and lisse subregular $mathcal {W}$-algebras in simply laced types. Third, for the latter cases we compute $mathcal {S}$-matrices and fusion rules. Our results provide the first examples of rational $mathcal {W}$-algebras associated with nonprincipal distinguished nilpotent elements, and the corresponding fusion rules are rather mysterious

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Details 詳細情報について

  • CRID
    1050297659216126464
  • ISSN
    14359863
    14359855
  • HANDLE
    2433/285245
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • IRDB

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